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A131607 Pell companion numbers A001333 without last digit. 2

%I #14 Jan 05 2020 21:43:05

%S 1,4,9,23,57,139,336,811,1960,4732,11424,27580,66585,160752,388089,

%T 936931,2261953,5460839,13183632,31828103,76839840,185507784,

%U 447855408,1081218600,2610292609,6301803820,15213900249,36729604319,88673108889,214075822099,516824753088

%N Pell companion numbers A001333 without last digit.

%H Andrew Howroyd, <a href="/A131607/b131607.txt">Table of n, a(n) for n = 4..1000</a>

%F a(n) = floor(A001333(n) / 10). - _Andrew Howroyd_, Jan 02 2020

%F Conjectures from _Colin Barker_, Jan 03 2020: (Start)

%F G.f.: x^4*(1 + x - 2*x^2 + x^3 + x^4) / ((1 - x)*(1 + x^2)*(1 - 2*x - x^2)*(1 - x^2 + x^4)).

%F a(n) = 3*a(n-1) - a(n-2) - a(n-3) - a(n-6) + 3*a(n-7) - a(n-8) - a(n-9) for n>12.

%F (End)

%t Table[Floor[(((1 - Sqrt[2])^n + (1 + Sqrt[2])^n)/2)/10], {n, 4, 29}] (* _Metin Sariyar_, Jan 03 2020 *)

%o (PARI) a(n)={polcoef((1 - x) / (1 - 2*x - x^2) + O(x*x^n), n)\10} \\ _Andrew Howroyd_, Jan 02 2020

%Y Cf. A001333, A131727.

%K nonn,base

%O 4,2

%A _Paul Curtz_, Oct 02 2007

%E Offset changed and terms a(24) and beyond from _Andrew Howroyd_, Jan 02 2020

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Last modified April 24 14:54 EDT 2024. Contains 371960 sequences. (Running on oeis4.)